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This is Part 4 of an ongoing investigation into the behaviour of 1-bit sigma-delta modulators. In this paper we question the usual concept of the ?average quantizer gain? as it applies to the quantizer transfer characteristic of a 1-bit modulator. We show that the concept is rather nebulous and does not help us to understand the operation of the 1-bit modulator. But our investigation of a number of possible alternative definitions of the gain shows that some of them do yield stable values which may have some significance.